Question

Find the cost price of an article sold by the shopkeeper on selling the article at Rs. 240?
% Statement 1 I. If the article sold at 25% more the profit earned will be Rs. 40.
% Statement 2 II. Marked price of article is Rs. 400 and profit percentage is equal to discount percentage offered and profit percentage is 40%.

• A. If the question can be answered by using statement I alone.
• B. If the question can be answered by using statement II alone.
• C. If the question can be answered by using both the statements together, but cannot be answered by either statement alone.
• D. If the question can be answered by using either statement I or statement II alone.
• E. If the question cannot be answered even by using both the statements together.

Hint:

When solving questions involving profit, discount, and selling price, always start with the basic relationships: \[ \text{Profit} = \text{Selling Price} - \text{Cost Price}, \quad \text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost Price}} \times 100, \quad \text{Discount} = \text{Marked Price} - \text{Selling Price}.\]

Answer 1

The Correct Option is C

Step 1: Understanding Statement I.
Statement I says: "If the article sold at 25% more, the profit earned will be Rs. 40." Let the cost price of the article be \( C \). According to this statement, the selling price at 25% more than Rs. 240 would be: \[ \text{New selling price} = 240 \times 1.25 = 300 \] The profit earned when sold at Rs. 300 would be Rs. 40. The profit is the difference between the selling price and the cost price: \[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \] Thus, \( 300 - C = 40 \), which gives: \[ C = 300 - 40 = 260 \] So, Statement I alone gives us the cost price \( C = 260 \). Step 2: Understanding Statement II.
Statement II says: "Marked price of article is Rs. 400 and profit percentage is equal to discount percentage offered." Let the cost price be \( C \) and the selling price be Rs. 240. The discount offered is the difference between the marked price and the selling price: \[ \text{Discount} = 400 - 240 = 160 \] The discount percentage is given by: \[ \text{Discount Percentage} = \frac{\text{Discount}}{\text{Marked Price}} \times 100 = \frac{160}{400} \times 100 = 40% \] According to Statement II, the profit percentage is equal to the discount percentage, so the profit percentage is also 40%. The profit percentage is given by: \[ \text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost Price}} \times 100 \] Since the profit percentage is 40%, we can set up the equation: \[ \frac{240 - C}{C} \times 100 = 40 \] Solving this equation: \[ \frac{240 - C}{C} = 0.4 \] \[ 240 - C = 0.4C \] \[ 240 = 1.4C \] \[ C = \frac{240}{1.4} = 171.43 \] So, Statement II alone gives us the cost price \( C = 171.43 \). Step 3: Combining Both Statements.
While each statement gives different values for the cost price, we can combine both statements to find a consistent value. Statement I suggests that the cost price is Rs. 260, and Statement II suggests that the cost price is Rs. 171.43. However, neither statement alone gives us the correct answer without the other statement. Step 4: Conclusion.
Therefore, the correct answer is (C) If the question can be answered by using both the statements together, but cannot be answered by either statement alone.